Design: Blocked RCT, with 2 levels, and randomization done at level 1 (individual level).

Models: Constant treatment effects, fixed treatment effects, and random treatment effects.

Power Validation

Default parameters:

M = 3
J = 20
rho: \(\rho\) = 0.5
ATE ES = 0.125, 0.125, 0.125
R2.1: \(R^2_1\) = 0, 0, 0

Parameters by model type:

Omega: \(\omega_2 = 0\) for constant effects, \(\omega_2\) = for fixed and random
ICC: \(\text{ICC}_2 = 0\) for constant and fixed effects, \(\text{ICC}_2\) = 0.2, 0.2, 0.2 for random effects

Assumptions:

Two-level design: \(\text{ICC}_3 = 0\), \(\omega_3 = 0\), \(K = 1\)

Varying school size

\(\bar{n}\) = 50

Varying R2

\(R^2_1 =\) 0.6, 0.6, 0.6

\(R^2_2 =\) 0.6, 0.6, 0.6 (This should not affect power!)

Varying rho

\(\rho =\) 0.2

\(\rho =\) 0.8

Varying true positives

ATE (ES) = 0.125, 0, 0

Varying ICC

\(\text{ICC}_2\) = 0.8, 0.8, 0.8

MDES validation

## 
## 
## +------------+---------------+-------------+-------------+
## |    MTP     | Adjusted MDES | Indiv Power | Target MDES |
## +============+===============+=============+=============+
## |    rawp    |     0.124     |    0.502    |    0.125    |
## +------------+---------------+-------------+-------------+
## | Bonferroni |     0.124     |    0.33     |    0.125    |
## +------------+---------------+-------------+-------------+
## |     BH     |     0.125     |    0.427    |    0.125    |
## +------------+---------------+-------------+-------------+
## |    Holm    |     0.123     |    0.381    |    0.125    |
## +------------+---------------+-------------+-------------+
## 
## Table: blocked_i1_2c

## 
## 
## +------------+---------------+-------------+-------------+
## |    MTP     | Adjusted MDES | Indiv Power | Target MDES |
## +============+===============+=============+=============+
## |    rawp    |     0.125     |    0.503    |    0.125    |
## +------------+---------------+-------------+-------------+
## | Bonferroni |     0.124     |    0.332    |    0.125    |
## +------------+---------------+-------------+-------------+
## |     BH     |     0.129     |    0.456    |    0.125    |
## +------------+---------------+-------------+-------------+
## |    Holm    |     0.123     |    0.383    |    0.125    |
## +------------+---------------+-------------+-------------+
## 
## Table: blocked_i1_2f

## 
## 
## +------------+---------------+-------------+-------------+
## |    MTP     | Adjusted MDES | Indiv Power | Target MDES |
## +============+===============+=============+=============+
## |    rawp    |     0.124     |    0.43     |    0.125    |
## +------------+---------------+-------------+-------------+
## | Bonferroni |     0.125     |    0.242    |    0.125    |
## +------------+---------------+-------------+-------------+
## |     BH     |     0.124     |    0.337    |    0.125    |
## +------------+---------------+-------------+-------------+
## |    Holm    |     0.125     |    0.291    |    0.125    |
## +------------+---------------+-------------+-------------+
## 
## Table: blocked_i1_2r

Sample size validation

## 
## 
## +------+-------------+-------------+---------------+--------------------+
## | MTP  | Sample type | Sample size | D1indiv power | Target sample size |
## +======+=============+=============+===============+====================+
## |  BH  |      J      |     20      |     0.425     |         20         |
## +------+-------------+-------------+---------------+--------------------+
## | Holm |      J      |     21      |     0.399     |         20         |
## +------+-------------+-------------+---------------+--------------------+
## |  BH  |    nbar     |     52      |     0.452     |         50         |
## +------+-------------+-------------+---------------+--------------------+
## | Holm |    nbar     |     52      |     0.41      |         50         |
## +------+-------------+-------------+---------------+--------------------+
## 
## Table: blocked_i1_2c

## 
## 
## +------+-------------+-------------+---------------+--------------------+
## | MTP  | Sample type | Sample size | D1indiv power | Target sample size |
## +======+=============+=============+===============+====================+
## |  BH  |      J      |     21      |     0.43      |         20         |
## +------+-------------+-------------+---------------+--------------------+
## | Holm |      J      |     21      |     0.398     |         20         |
## +------+-------------+-------------+---------------+--------------------+
## |  BH  |    nbar     |     53      |     0.454     |         50         |
## +------+-------------+-------------+---------------+--------------------+
## | Holm |    nbar     |     49      |     0.379     |         50         |
## +------+-------------+-------------+---------------+--------------------+
## 
## Table: blocked_i1_2f

## 
## 
## +------+-------------+-------------+---------------+--------------------+
## | MTP  | Sample type | Sample size | D1indiv power | Target sample size |
## +======+=============+=============+===============+====================+
## |  BH  |      J      |     20      |     0.34      |         20         |
## +------+-------------+-------------+---------------+--------------------+
## | Holm |      J      |     21      |     0.309     |         20         |
## +------+-------------+-------------+---------------+--------------------+
## |  BH  |    nbar     |     49      |     0.333     |         50         |
## +------+-------------+-------------+---------------+--------------------+
## | Holm |    nbar     |     50      |     0.288     |         50         |
## +------+-------------+-------------+---------------+--------------------+
## 
## Table: blocked_i1_2r

Validate Power: blocked_i1_2cfr

Kristin Porter, Zarni Htet, Kristen Hunter

January 10, 2021